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Principal Component Analysis in Bayes Spaces for Sparsely Sampled Density Functions.

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Τίτλος: Principal Component Analysis in Bayes Spaces for Sparsely Sampled Density Functions.
Συγγραφείς: Steyer, Lisa1 (AUTHOR) lisa.steyer@hu-berlin.de, Greven, Sonja1 (AUTHOR)
Πηγή: Journal of Computational & Graphical Statistics. Aug2026, p1-12. 12p. 3 Illustrations.
Θεματικοί όροι: *Functional analysis, Probability density function, Gaussian processes, Expectation-maximization algorithms, Data transformations (Statistics), Principal components analysis, Sampling errors
Περίληψη: This article presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces, where densities are the object of analysis, but only few individual samples from each density are observed. We use the observed data directly to account for all sources of uncertainty, instead of relying on prior estimation of the underlying densities in a two-step approach, which can be inaccurate if small or heterogeneous numbers of samples per density are available. To account for the constrained nature of densities, we base our approach on Bayes spaces, which extend the Aitchison geometry for compositional data to density functions. For modeling, we exploit the isometric isomorphism between the Bayes space and the L2 subspace L02 with integration-to-zero constraint through the centered log-ratio (clr) transformation. As only discrete draws from each density are observed, we treat the underlying densities as latent variables within a maximum likelihood framework, based on a Gaussian process assumption with finite basis expansion for their clr-transformations, and employ a Monte Carlo Expectation Maximization (MCEM) algorithm for model estimation. We apply the method to rental price distributions across Munich districts and maximum daily summer temperatures in Berlin over the past 70 years. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational & Graphical Statistics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Principal Component Analysis in Bayes Spaces for Sparsely Sampled Density Functions.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+%26+Graphical+Statistics%22">Journal of Computational & Graphical Statistics</searchLink>. Aug2026, p1-12. 12p. 3 Illustrations.
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  Data: *<searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+density+function%22">Probability density function</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+processes%22">Gaussian processes</searchLink><br /><searchLink fieldCode="DE" term="%22Expectation-maximization+algorithms%22">Expectation-maximization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Data+transformations+%28Statistics%29%22">Data transformations (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Principal+components+analysis%22">Principal components analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Sampling+errors%22">Sampling errors</searchLink>
– Name: Abstract
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  Data: This article presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces, where densities are the object of analysis, but only few individual samples from each density are observed. We use the observed data directly to account for all sources of uncertainty, instead of relying on prior estimation of the underlying densities in a two-step approach, which can be inaccurate if small or heterogeneous numbers of samples per density are available. To account for the constrained nature of densities, we base our approach on Bayes spaces, which extend the Aitchison geometry for compositional data to density functions. For modeling, we exploit the isometric isomorphism between the Bayes space and the L2 subspace L02 with integration-to-zero constraint through the centered log-ratio (clr) transformation. As only discrete draws from each density are observed, we treat the underlying densities as latent variables within a maximum likelihood framework, based on a Gaussian process assumption with finite basis expansion for their clr-transformations, and employ a Monte Carlo Expectation Maximization (MCEM) algorithm for model estimation. We apply the method to rental price distributions across Munich districts and maximum daily summer temperatures in Berlin over the past 70 years. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational & Graphical Statistics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/10618600.2026.2709742
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 1
    Subjects:
      – SubjectFull: Functional analysis
        Type: general
      – SubjectFull: Probability density function
        Type: general
      – SubjectFull: Gaussian processes
        Type: general
      – SubjectFull: Expectation-maximization algorithms
        Type: general
      – SubjectFull: Data transformations (Statistics)
        Type: general
      – SubjectFull: Principal components analysis
        Type: general
      – SubjectFull: Sampling errors
        Type: general
    Titles:
      – TitleFull: Principal Component Analysis in Bayes Spaces for Sparsely Sampled Density Functions.
        Type: main
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            NameFull: Steyer, Lisa
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            NameFull: Greven, Sonja
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          Dates:
            – D: 04
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 10618600
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            – TitleFull: Journal of Computational & Graphical Statistics
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